2.1 Mental Math Mental math: -Solidifies understanding of place value, as in the problem 52x10=_ -Teaches how numbers can be rearranged and manipulated according to the any-order and distributive property. -Demonstrates how the same answer can often be re
5.4 More on Primes: Fact 4.1 (Primality test) Thus to test whether N is prime one need to check divisibility by t he primes. Example is 179 prime. -142 =196 -179 is not divisibility by 2,3,5,7,11,13 -Thus 179 is prime. T heorem 4.5 There are infinitely ma
5.5 2* 2* 3. hus, Thus, the LCM isGreatest Common Factors and Least Common Multiple: the Greatest Common Factor is 6. The Greatest common factor of two whole numbers a and b, written GCF (a,b) is the greatest whole number which is a factor of both a and b
6.2 notes: (More Fraction Basics) Stage 6- M ixed numbers and improper fractions: fractions greater than one can be wri t ten either as mixed numbers or improper fractions. M ixed Number- 2 1/8 Improper Fraction- 8/5 Stage 7- Fractions as an expression of
6.3 notes:
Teaching sequence: Step one: whole number times a fraction 3*1/4=3/4 Step two: Fraction times a whole number 1/4 * 3= Step three: fraction t imes a fraction Rule four: a/b*c/d=ac/bd (Factor and cancel out before multiplying) Measurement Divisio
1/6 ?
Notes 6.4 Division of Fractions:
Teaching Sequence1) Dividing a whole number by a whole number a. Example 4.1 T wo girls share 5 cookies equally. How much did each girl get?
This is a parti tive question asking us to find 52. Calculations 52=5 halfs
Notes 6.5 Division Word Problems: Rule 5: a/b c/b= a c Invert and mult iply Rule: a / b c / d= a/b x d/c Parti tive division explanation: 6 is of what numbers? Measurement division explanation: How many units of size s make 6? Pre-algebra explanation: by
2.3 T he A r t of Word P roblems:
Word problems need to be: -Short, clear, and succinct -In teresting -Realistic or whimsical -Self contained with a single answer Features of a Teachers Solution: 1. All given information is labeled on the picture and the
4) (2 points each) Show how to calculate the following using Mental Math techniques that involve,
either squares of numbers up to 20
or powers of 2 up to the tenth power
or arithmetic identities including squares of sums/differences, differences of square
5.3 Primes and the Fundamental Theorem of Arithmetic
A prime number is a whole number p >1 whose only factors are 1 and p. Whole numbers N >2 which are not prime are called composite. P rimes: 2,3,5,7,11,13,17,19,23,27,29 This method is called the Sieve o
5.2 Divisibility TestsWe say A is divisible by K whenever A is a multiple of K, that is, if A= K *a for some whole n umber a. The following phrases all have the same meaning: 1) A is divisible by K 2) K divides A 3) A is a multiple of K 4) K is a factor o
1.6-Division
Division- related to multiplication by Missing Factor *4 factor families5x7=35 7x5=35 35/5=7 35/7=5 a/b=c (a=dividend, b=divisor, c=quotient) Two types of interpretation: (pg. 32) -Parti tive division- 20 is 4 of what group -Measurement divis
1.5 Multiplication Multiplication- multiplication of whole numbers is repeated addition. Set Model-
Measurement Model-
0
6
12
-Two steps of six
Rectangular ModelX X X X (1x4=4) Multiplication Properties:
1. Multiplication Identity Property- 5x1=5 2. Commu
1.4 Subtraction Subtraction- defined by missing addends: 13-5 is the number that fi ts in the blank. Ex: 5+_=13 Part- Whole In terpretation: a part of a set or quantity is specified and we want to know how m uch is needed to make i t whole. Thus, we must
1.3 Addition Any-Order property- a list of whole numbers can be added in any order. Thus 3+6+2 can be computed as (3+6) +2 or (2+3) +6, etc. Additive Identity property- 5+0=5 Commutative property-7+5=5+7 Associative property-(3+7)+5=3+(7+5) Thinking Strat
1.2- The place value process The place value processi)Form bundles of 1, 10, 100, 1000, etc. ii)If necessary rebundle to ensure that there are at most 9 bundles of each denomination. iii)Count the number of each denomination and record that number in the
M ath Chapter One:
1.1 Counting Whole Numbers- The numbers we use to count beginning with zero. 0,1,2,3. Set Model- Concrete objects; the answer most be a whole number. M easurement Model- used for distance, t ime, weight, and height. NumeralsTallies-The
Chapter 3: Algorithms- is a systematic step by step procedure to solve a class of problems. A mathematical algorithm is a cyclic computation algorithm, which solves problems, is a finite number of steps. 3.1- The Addition Algorithm- The addition algorithm
Chapter Four:
Pre-algebra: Simply arithmetic with one new feature: we use letters to represent numbers
4.1- It is often useful to represent numbers. This is the case when: -The number is unknown -We want to state relationships which hold for all numbers -
2.2 Word P roblemsTeaching Sequence- Word problems can be difficult because they involve three steps: 1) Converting the word problem to an arithmetic or algebra problem. 2) Solving the arithmetic or algebra problem 3) Interpreting the solution to obtain a
Name
December 17, 2003
Math T101
Final Exam
Do all 27 problems (200 points total). Place your answers in the spaces provided. You must show
your work to receive credit. No calculators allowed.
(1) (5 points)
3
5
14
1 + 25
Express the fraction in simplest